xf.li | bdd93d5 | 2023-05-12 07:10:14 -0700 | [diff] [blame^] | 1 | /* Complex hyperbole tangent for double. |
| 2 | Copyright (C) 1997-2016 Free Software Foundation, Inc. |
| 3 | This file is part of the GNU C Library. |
| 4 | Contributed by Ulrich Drepper <drepper@cygnus.com>, 1997. |
| 5 | |
| 6 | The GNU C Library is free software; you can redistribute it and/or |
| 7 | modify it under the terms of the GNU Lesser General Public |
| 8 | License as published by the Free Software Foundation; either |
| 9 | version 2.1 of the License, or (at your option) any later version. |
| 10 | |
| 11 | The GNU C Library is distributed in the hope that it will be useful, |
| 12 | but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
| 14 | Lesser General Public License for more details. |
| 15 | |
| 16 | You should have received a copy of the GNU Lesser General Public |
| 17 | License along with the GNU C Library; if not, see |
| 18 | <http://www.gnu.org/licenses/>. */ |
| 19 | |
| 20 | #include <complex.h> |
| 21 | #include <fenv.h> |
| 22 | #include <math.h> |
| 23 | #include <math_private.h> |
| 24 | #include <float.h> |
| 25 | |
| 26 | __complex__ double |
| 27 | __ctanh (__complex__ double x) |
| 28 | { |
| 29 | __complex__ double res; |
| 30 | |
| 31 | if (__glibc_unlikely (!isfinite (__real__ x) || !isfinite (__imag__ x))) |
| 32 | { |
| 33 | if (isinf (__real__ x)) |
| 34 | { |
| 35 | __real__ res = __copysign (1.0, __real__ x); |
| 36 | if (isfinite (__imag__ x) && fabs (__imag__ x) > 1.0) |
| 37 | { |
| 38 | double sinix, cosix; |
| 39 | __sincos (__imag__ x, &sinix, &cosix); |
| 40 | __imag__ res = __copysign (0.0, sinix * cosix); |
| 41 | } |
| 42 | else |
| 43 | __imag__ res = __copysign (0.0, __imag__ x); |
| 44 | } |
| 45 | else if (__imag__ x == 0.0) |
| 46 | { |
| 47 | res = x; |
| 48 | } |
| 49 | else |
| 50 | { |
| 51 | __real__ res = __nan (""); |
| 52 | __imag__ res = __nan (""); |
| 53 | |
| 54 | if (isinf (__imag__ x)) |
| 55 | feraiseexcept (FE_INVALID); |
| 56 | } |
| 57 | } |
| 58 | else |
| 59 | { |
| 60 | double sinix, cosix; |
| 61 | double den; |
| 62 | const int t = (int) ((DBL_MAX_EXP - 1) * M_LN2 / 2); |
| 63 | |
| 64 | /* tanh(x+iy) = (sinh(2x) + i*sin(2y))/(cosh(2x) + cos(2y)) |
| 65 | = (sinh(x)*cosh(x) + i*sin(y)*cos(y))/(sinh(x)^2 + cos(y)^2). */ |
| 66 | |
| 67 | if (__glibc_likely (fabs (__imag__ x) > DBL_MIN)) |
| 68 | { |
| 69 | __sincos (__imag__ x, &sinix, &cosix); |
| 70 | } |
| 71 | else |
| 72 | { |
| 73 | sinix = __imag__ x; |
| 74 | cosix = 1.0; |
| 75 | } |
| 76 | |
| 77 | if (fabs (__real__ x) > t) |
| 78 | { |
| 79 | /* Avoid intermediate overflow when the imaginary part of |
| 80 | the result may be subnormal. Ignoring negligible terms, |
| 81 | the real part is +/- 1, the imaginary part is |
| 82 | sin(y)*cos(y)/sinh(x)^2 = 4*sin(y)*cos(y)/exp(2x). */ |
| 83 | double exp_2t = __ieee754_exp (2 * t); |
| 84 | |
| 85 | __real__ res = __copysign (1.0, __real__ x); |
| 86 | __imag__ res = 4 * sinix * cosix; |
| 87 | __real__ x = fabs (__real__ x); |
| 88 | __real__ x -= t; |
| 89 | __imag__ res /= exp_2t; |
| 90 | if (__real__ x > t) |
| 91 | { |
| 92 | /* Underflow (original real part of x has absolute value |
| 93 | > 2t). */ |
| 94 | __imag__ res /= exp_2t; |
| 95 | } |
| 96 | else |
| 97 | __imag__ res /= __ieee754_exp (2 * __real__ x); |
| 98 | } |
| 99 | else |
| 100 | { |
| 101 | double sinhrx, coshrx; |
| 102 | if (fabs (__real__ x) > DBL_MIN) |
| 103 | { |
| 104 | sinhrx = __ieee754_sinh (__real__ x); |
| 105 | coshrx = __ieee754_cosh (__real__ x); |
| 106 | } |
| 107 | else |
| 108 | { |
| 109 | sinhrx = __real__ x; |
| 110 | coshrx = 1.0; |
| 111 | } |
| 112 | |
| 113 | if (fabs (sinhrx) > fabs (cosix) * DBL_EPSILON) |
| 114 | den = sinhrx * sinhrx + cosix * cosix; |
| 115 | else |
| 116 | den = cosix * cosix; |
| 117 | __real__ res = sinhrx * coshrx / den; |
| 118 | __imag__ res = sinix * cosix / den; |
| 119 | } |
| 120 | math_check_force_underflow_complex (res); |
| 121 | } |
| 122 | |
| 123 | return res; |
| 124 | } |
| 125 | weak_alias (__ctanh, ctanh) |
| 126 | #ifdef NO_LONG_DOUBLE |
| 127 | strong_alias (__ctanh, __ctanhl) |
| 128 | weak_alias (__ctanh, ctanhl) |
| 129 | #endif |